Chapter 1. Introduction Chapter 2. Poissonization and de-Poissonization Chapter 3. Permutations and Young tableaux Chapter 4. Bounds of the expected value of $\ell _N$ Chapter 5. Orthogonal polynomials, Riemann-Hilbert problems, and Toeplitz matrices Chapter 6. Random matrix theory Chapter 7. Toeplitz determinant formula Chapter 8. Fredholm determinant formula Chapter 9. Asymptotic results Chapter 10. Schur measure and directed last passage percolation Chapter 11. Determinantal point processes Chapter 12. Tiling of the Aztec diamond Chapter 13. The Dyson process and Brownian Dyson process Appendix A. Theory of trace class operators and Fredholm determinants Appendix B. Steepest-descent method for the asymptotic evaluation of integrals in the complex plane Appendix C. Basic results of stochastic calculus

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Electronic reproduction. Providence, Rhode Island : American Mathematical Society. 2016